Next week, I will be teaching Math 246A, the first course in the three-quarter graduate complex analysis sequence. This first course covers much of the same ground as an honours undergraduate complex analysis course, in particular focusing on the basic properties of holomorphic functions such as the Cauchy and residue theorems, the classification of singularities, and the maximum principle, but there will be more of an emphasis on rigour, generalisation and abstraction, and connections with other parts of mathematics. If time permits I may also cover topics such as factorisation theorems, harmonic functions, conformal mapping, and/or applications to analytic number theory. The main text I will be using for this course is Stein-Shakarchi (with Ahlfors as a secondary text), but as usual I will also be writing notes for the course on this blog.

### Recent Comments

Ryan on 246A, Notes 0: the complex… | |

dn1214 on Nonlinear dispersive equations… | |

Typo? on Moser’s entropy compress… | |

William Deng on Analysis I | |

William Deng on Analysis I | |

¿En dónde está el ce… on Hilbert’s nullstellensat… | |

William Deng on Analysis I | |

Hubert Schaetzel on Almost all Collatz orbits atta… | |

aquazorcarson on Boosting the van der Corput in… | |

aquazorcarson on Boosting the van der Corput in… | |

James on A quantitative formulation of… | |

SCHAETZEL Hubert on Almost all Collatz orbits atta… | |

Euiwoong Lee on Topics in random matrix t… | |

Marcel Goh on Additive combinatorics | |

William Deng on Analysis I |

### Articles by others

- Andreas Blass – The mathematical theory T of actual mathematical reasoning
- Gene Weingarten – Pearls before breakfast
- Isaac Asimov – The relativity of wrong
- Jonah Lehrer – Don't! – the secret of self-control
- Julianne Dalcanton – The cult of genius
- Nassim Taleb – The fourth quadrant: a map of the limits of statistics
- Paul Graham – What You'll Wish You'd Known
- Po Bronson – How not to talk to your kids
- Scott Aaronson – Ten signs a claimed mathematical proof is wrong
- Tanya Klowden – articles on astronomy
- Timothy Gowers – Elsevier — my part in its downfall
- Timothy Gowers – The two cultures of mathematics
- William Thurston – On proof and progress in mathematics

### Diversions

- Abstruse Goose
- BoxCar2D
- Factcheck.org
- FiveThirtyEight
- Gapminder
- Literally Unbelievable
- Planarity
- PolitiFact
- Quite Interesting
- snopes
- Strange maps
- Television tropes and idioms
- The Economist
- The Onion
- The Straight Dope
- This American Life on the financial crisis I
- This American Life on the financial crisis II
- What if? (xkcd)
- xkcd

### Mathematics

- 0xDE
- A Mind for Madness
- A Portion of the Book
- Absolutely useless
- Alex Sisto
- Algorithm Soup
- Almost Originality
- AMS blogs
- AMS Graduate Student Blog
- Analysis & PDE
- Analysis & PDE Conferences
- Annoying Precision
- Area 777
- Ars Mathematica
- ATLAS of Finite Group Representations
- Automorphic forum
- Avzel's journal
- Blog on Math Blogs
- blogderbeweise
- Bubbles Bad; Ripples Good
- Cédric Villani
- Climbing Mount Bourbaki
- Coloquio Oleis
- Combinatorics and more
- Compressed sensing resources
- Computational Complexity
- Concrete nonsense
- David Mumford's blog
- Delta epsilons
- DispersiveWiki
- Disquisitiones Mathematicae
- Embûches tissues
- Emmanuel Kowalski’s blog
- Equatorial Mathematics
- fff
- Floer Homology
- Frank Morgan’s blog
- Gérard Besson's Blog
- Gödel’s Lost Letter and P=NP
- Geometric Group Theory
- Geometry and the imagination
- Geometry Bulletin Board
- George Shakan
- Girl's Angle
- God Plays Dice
- Good Math, Bad Math
- Graduated Understanding
- Hydrobates
- I Can't Believe It's Not Random!
- I Woke Up In A Strange Place
- Igor Pak's blog
- Images des mathématiques
- In theory
- James Colliander's Blog
- Jérôme Buzzi’s Mathematical Ramblings
- Joel David Hamkins
- Journal of the American Mathematical Society
- Kill Math
- Le Petit Chercheur Illustré
- Lemma Meringue
- Lewko's blog
- Libres pensées d’un mathématicien ordinaire
- LMS blogs page
- Low Dimensional Topology
- M-Phi
- Mark Sapir's blog
- Math Overflow
- Math3ma
- Math3ma
- Mathbabe
- Mathblogging
- Mathematical musings
- Mathematics Illuminated
- Mathematics in Australia
- Mathematics Jobs Wiki
- Mathematics Stack Exchange
- Mathematics under the Microscope
- Mathematics without apologies
- Mathlog
- Mathtube
- Matt Baker's Math Blog
- Mixedmath
- Motivic stuff
- Much ado about nothing
- Multiple Choice Quiz Wiki
- MyCQstate
- nLab
- Noncommutative geometry blog
- Nonlocal equations wiki
- Nuit-blanche
- Number theory web
- Online Analysis Research Seminar
- outofprintmath
- Pattern of Ideas
- Pengfei Zhang's blog
- Persiflage
- Peter Cameron's Blog
- Phillipe LeFloch's blog
- ProofWiki
- Quomodocumque
- Ramis Movassagh's blog
- Random Math
- Reasonable Deviations
- Regularize
- Research Seminars
- Rigorous Trivialities
- Roots of unity
- Science Notes by Greg Egan
- Secret Blogging Seminar
- Selected Papers Network
- Sergei Denisov's blog
- Short, Fat Matrices
- Shtetl-Optimized
- Shuanglin's Blog
- Since it is not…
- Sketches of topology
- Snapshots in Mathematics !
- Soft questions
- Some compact thoughts
- Stacks Project Blog
- SymOmega
- Tanya Khovanova's Math Blog
- tcs math
- TeX, LaTeX, and friends
- The accidental mathematician
- The Cost of Knowledge
- The Everything Seminar
- The Geomblog
- The L-function and modular forms database
- The n-Category Café
- The n-geometry cafe
- The On-Line Blog of Integer Sequences
- The polylogblog
- The polymath blog
- The polymath wiki
- The Tricki
- The twofold gaze
- The Unapologetic Mathematician
- The value of the variable
- The World Digital Mathematical Library
- Theoretical Computer Science – StackExchange
- Tim Gowers’ blog
- Tim Gowers’ mathematical discussions
- Todd and Vishal’s blog
- Van Vu's blog
- Vaughn Climenhaga
- Vieux Girondin
- Visual Insight
- Vivatsgasse 7
- Williams College Math/Stat Blog
- Windows on Theory
- Wiskundemeisjes
- XOR’s hammer
- Yufei Zhao's blog
- Zhenghe's Blog

### Selected articles

- A cheap version of nonstandard analysis
- A review of probability theory
- American Academy of Arts and Sciences speech
- Amplification, arbitrage, and the tensor power trick
- An airport-inspired puzzle
- Benford's law, Zipf's law, and the Pareto distribution
- Compressed sensing and single-pixel cameras
- Einstein’s derivation of E=mc^2
- On multiple choice questions in mathematics
- Problem solving strategies
- Quantum mechanics and Tomb Raider
- Real analysis problem solving strategies
- Sailing into the wind, or faster than the wind
- Simons lectures on structure and randomness
- Small samples, and the margin of error
- Soft analysis, hard analysis, and the finite convergence principle
- The blue-eyed islanders puzzle
- The cosmic distance ladder
- The federal budget, rescaled
- Ultrafilters, non-standard analysis, and epsilon management
- What is a gauge?
- What is good mathematics?
- Why global regularity for Navier-Stokes is hard

### Software

### The sciences

### Top Posts

- Career advice
- Does one have to be a genius to do maths?
- Books
- There’s more to mathematics than rigour and proofs
- On writing
- About
- The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation
- On "compilation errors" in mathematical reading, and how to resolve them
- Moser's entropy compression argument
- Work hard

### Archives

- February 2021 (6)
- January 2021 (2)
- December 2020 (4)
- November 2020 (2)
- October 2020 (4)
- September 2020 (5)
- August 2020 (2)
- July 2020 (2)
- June 2020 (1)
- May 2020 (2)
- April 2020 (3)
- March 2020 (9)
- February 2020 (1)
- January 2020 (3)
- December 2019 (4)
- November 2019 (2)
- September 2019 (2)
- August 2019 (3)
- July 2019 (2)
- June 2019 (4)
- May 2019 (6)
- April 2019 (4)
- March 2019 (2)
- February 2019 (5)
- January 2019 (1)
- December 2018 (6)
- November 2018 (2)
- October 2018 (2)
- September 2018 (5)
- August 2018 (3)
- July 2018 (3)
- June 2018 (1)
- May 2018 (4)
- April 2018 (4)
- March 2018 (5)
- February 2018 (4)
- January 2018 (5)
- December 2017 (5)
- November 2017 (3)
- October 2017 (4)
- September 2017 (4)
- August 2017 (5)
- July 2017 (5)
- June 2017 (1)
- May 2017 (3)
- April 2017 (2)
- March 2017 (3)
- February 2017 (1)
- January 2017 (2)
- December 2016 (2)
- November 2016 (2)
- October 2016 (5)
- September 2016 (4)
- August 2016 (4)
- July 2016 (1)
- June 2016 (3)
- May 2016 (5)
- April 2016 (2)
- March 2016 (6)
- February 2016 (2)
- January 2016 (1)
- December 2015 (4)
- November 2015 (6)
- October 2015 (5)
- September 2015 (5)
- August 2015 (4)
- July 2015 (7)
- June 2015 (1)
- May 2015 (5)
- April 2015 (4)
- March 2015 (3)
- February 2015 (4)
- January 2015 (4)
- December 2014 (6)
- November 2014 (5)
- October 2014 (4)
- September 2014 (3)
- August 2014 (4)
- July 2014 (5)
- June 2014 (5)
- May 2014 (5)
- April 2014 (2)
- March 2014 (4)
- February 2014 (5)
- January 2014 (4)
- December 2013 (4)
- November 2013 (5)
- October 2013 (4)
- September 2013 (5)
- August 2013 (1)
- July 2013 (7)
- June 2013 (12)
- May 2013 (4)
- April 2013 (2)
- March 2013 (2)
- February 2013 (6)
- January 2013 (1)
- December 2012 (4)
- November 2012 (7)
- October 2012 (6)
- September 2012 (4)
- August 2012 (3)
- July 2012 (4)
- June 2012 (3)
- May 2012 (3)
- April 2012 (4)
- March 2012 (5)
- February 2012 (5)
- January 2012 (4)
- December 2011 (8)
- November 2011 (8)
- October 2011 (7)
- September 2011 (6)
- August 2011 (8)
- July 2011 (9)
- June 2011 (8)
- May 2011 (11)
- April 2011 (3)
- March 2011 (10)
- February 2011 (3)
- January 2011 (5)
- December 2010 (5)
- November 2010 (6)
- October 2010 (9)
- September 2010 (9)
- August 2010 (3)
- July 2010 (4)
- June 2010 (8)
- May 2010 (8)
- April 2010 (8)
- March 2010 (8)
- February 2010 (10)
- January 2010 (12)
- December 2009 (11)
- November 2009 (8)
- October 2009 (15)
- September 2009 (6)
- August 2009 (13)
- July 2009 (10)
- June 2009 (11)
- May 2009 (9)
- April 2009 (11)
- March 2009 (14)
- February 2009 (13)
- January 2009 (18)
- December 2008 (8)
- November 2008 (9)
- October 2008 (10)
- September 2008 (5)
- August 2008 (6)
- July 2008 (7)
- June 2008 (8)
- May 2008 (11)
- April 2008 (12)
- March 2008 (12)
- February 2008 (13)
- January 2008 (17)
- December 2007 (10)
- November 2007 (9)
- October 2007 (9)
- September 2007 (7)
- August 2007 (9)
- July 2007 (9)
- June 2007 (6)
- May 2007 (10)
- April 2007 (11)
- March 2007 (9)
- February 2007 (4)

### Categories

- expository (288)
- tricks (11)

- guest blog (10)
- Mathematics (813)
- math.AC (8)
- math.AG (41)
- math.AP (112)
- math.AT (17)
- math.CA (175)
- math.CO (179)
- math.CT (7)
- math.CV (37)
- math.DG (37)
- math.DS (83)
- math.FA (24)
- math.GM (12)
- math.GN (21)
- math.GR (86)
- math.GT (16)
- math.HO (12)
- math.IT (13)
- math.LO (50)
- math.MG (43)
- math.MP (28)
- math.NA (23)
- math.NT (179)
- math.OA (22)
- math.PR (101)
- math.QA (6)
- math.RA (40)
- math.RT (21)
- math.SG (4)
- math.SP (48)
- math.ST (8)

- non-technical (164)
- admin (45)
- advertising (42)
- diversions (4)
- media (13)
- journals (3)

- obituary (15)

- opinion (31)
- paper (216)
- question (123)
- polymath (85)

- talk (67)
- DLS (20)

- teaching (188)
- 245A – Real analysis (11)
- 245B – Real analysis (21)
- 245C – Real analysis (6)
- 246A – complex analysis (11)
- 246B – complex analysis (5)
- 246C – complex analysis (5)
- 247B – Classical Fourier Analysis (5)
- 254A – analytic prime number theory (19)
- 254A – ergodic theory (18)
- 254A – Hilbert's fifth problem (12)
- 254A – Incompressible fluid equations (5)
- 254A – random matrices (14)
- 254B – expansion in groups (8)
- 254B – Higher order Fourier analysis (9)
- 255B – incompressible Euler equations (2)
- 275A – probability theory (6)
- 285G – poincare conjecture (20)
- Logic reading seminar (8)

- travel (26)

additive combinatorics
almost orthogonality
announcement
approximate groups
arithmetic progressions
Ben Green
Cauchy-Schwarz
Cayley graphs
central limit theorem
Chowla conjecture
compactness
compressed sensing
correspondence principle
distributions
eigenvalues
Elias Stein
Emmanuel Breuillard
entropy
equidistribution
ergodic theory
Euler equations
expander graphs
exponential sums
finite fields
Fourier transform
Freiman's theorem
Gowers uniformity norms
graph theory
Gromov's theorem
GUE
hard analysis
Hilbert's fifth problem
hypergraphs
incompressible Euler equations
inverse conjecture
Kaisa Matomaki
Kakeya conjecture
Lie algebras
Lie groups
Liouville function
Littlewood-Offord problem
Maksym Radziwill
Mobius function
multiple recurrence
Navier-Stokes equations
nilpotent groups
nilsequences
nonstandard analysis
parity problem
politics
polymath1
polymath8
Polymath15
polynomial method
polynomials
prime gaps
prime numbers
prime number theorem
random matrices
randomness
Ratner's theorem
regularity lemma
Ricci flow
Riemann zeta function
Roth's theorem
Schrodinger equation
sieve theory
structure
Szemeredi's theorem
Tamar Ziegler
ultrafilters
universality
Van Vu
wave maps
Yitang Zhang

### The Polymath Blog

- Polymath projects 2021 20 February, 2021
- A sort of Polymath on a famous MathOverflow problem 9 June, 2019
- Ten Years of Polymath 3 February, 2019
- Updates and Pictures 19 October, 2018
- Polymath proposal: finding simpler unit distance graphs of chromatic number 5 10 April, 2018
- A new polymath proposal (related to the Riemann Hypothesis) over Tao’s blog 26 January, 2018
- Spontaneous Polymath 14 – A success! 26 January, 2018
- Polymath 13 – a success! 22 August, 2017
- Non-transitive Dice over Gowers’s Blog 15 May, 2017
- Rota’s Basis Conjecture: Polymath 12, post 3 5 May, 2017

## 11 comments

Comments feed for this article

12 September, 2016 at 12:07 am

Lino VariVery much look forward to it Terry.

12 September, 2016 at 5:33 am

Lars EricsonWhen are you going to get that on EdX or Coursera?

12 September, 2016 at 6:40 am

Chris AldrichIt’s not as advanced a treatment, but if you’re looking for a complex analysis MOOC (on Coursera), there’s a class starting shortly: https://www.coursera.org/learn/complex-analysis

12 September, 2016 at 7:10 am

Lars EricsonI know Coursera has Complex Analysis, point of my comment was to encourage Prof. Tao to find a MOOC platform that offers free courses with grading and extend his teaching to the world in that way. Coursera is actually moving towards “monetizing” so they push you towards their for-pay options. Stanford’s Lagunita platform preserves the original ethos of Coursera which is to donate some education to the world.

12 September, 2016 at 6:45 am

GAYOUBCan you please tell me about EdX or Coursera?

12 September, 2016 at 7:07 am

Lars EricsonCoursera has a Complex Analysis course: https://www.coursera.org/learn/complex-analysis

Stanford has a for-pay EdX platform and a free platform called Lagunita: https://lagunita.stanford.edu/courses It is fairly sparse on pure math courses.

In general the core pure math courses with grading are few and far between in the MOOC world. There are a lot more technical MOOCs in applied math and applied science than in pure math and basic math (undergrad bread-and-butter core math courses). So you’ll get a Data Science with Python in many versions but no Calc 3.

UCLA is not a leader in MOOCs with very few free MOOCs on any platform.

12 September, 2016 at 5:57 am

miklos kontraThank s Profesor Tao, I m working on a connection between prime numbers and the Collatz Conjecture, I ve found a way that shows that the conjecture is true for every Natural number, really i found a way mixing graph theory some very basic algebra and logical math ( the idea was to use this mixture, the idea is based on what Paul Erdoss said about the conjecture ‘Mathematics are not ready for this kind of problem’ ‘Paul is a man of the same country as my fathers Hungary’, thats why i tried other things after 3 years of hard working trying out all kinds of things in math (series etc..) and reading many papers from Connway, Feinman even works published in arxiv and other sites, i will be presenting my thesis in computer science in december in Argentina University of UNLAM, if it is of your interest I can send you a copy of about 10 pages of the work on the Conjecture, I know that you re very busy, but just in case it might be of some help in your works.

The graphs shows the zones where mathematics can t explain the conjecture, but also shows that every number reach 1 having only 1 trivial cycle (4,2,1) and none of the paths diverge! If one takes out the cycle (4,2,1) the graph obeys as a tree structure where each node gets to 1.

Well I d would be very pleased if i could get somo feedback from you and add your opinion with your authorization to the thesis.

Thank s for youre time

Ing. Miklos Kontra

Buenos Aires, Argentina.

________________________________ De: Whats new Enviado: lunes, 12 de septiembre de 2016 03:11 a.m. Para: mkontra@hotmail.com Asunto: [New post] Course announcement: 246A, complex analysis

Terence Tao posted: “Next week, I will be teaching Math 246A, the first course in the three-quarter graduate complex analysis sequence. This first course covers much of the same ground as an honours undergraduate complex analysis course, in particular focusing on the basic p”

13 September, 2016 at 5:35 am

JDMthere are new textbooks and newer textbooks on the matter. Certainly:

Needham “Visual Complex Analysis”

https://www.amazon.com/Visual-Complex-Analysis-Tristan-Needham/dp/0198534469

This might not be at the level of the course. There is a textbook that teaches it via fluid mechanics ( I can’t find it… ) but I found these notes

and these are substantially less visual. “Introduction to Mathematical Fluid Mechanics”

16 September, 2016 at 11:58 am

jheavner724Neither of these are suitable at the graduate level. Needham’s text is nice, and it can be helpful for beginners who want to have some proficiency with complex variables, but it makes not for a course in rigorous complex analysis. The other texts are even less suitable for this sort of course. They may be excellent resources for scientists interested in fluid mechanics and complex analysis, but they once again lack the rigor demanded of pure mathematics.

Aflhors’ text is a classic, but one that may disdain; Tao’s choice of Stein is probably a perfect one. It is a very well written text authored by a master of analysis who Tao himself studied under; it retains rigor while also not being horribly terse or boring. Students will probably end up referencing Rudin, Alfhors, and Conway as well, but Stein may be the best leading text choice.

13 September, 2016 at 5:38 am

Romain ViguierI would like to find a field where we do not need too many data even if I know we cant replace thousands years of mathematics. I would like to learn few things with big scopes.

15 September, 2016 at 7:32 pm

alienbot007I remember when I was a kid I couldn’t solve a math problem, but then when I approached the problem later, I was able to understand it immediately. If I had never approached the problem again, I might have concluded that I was incapable of learning the concept.

In the interests of helping math become more accessible to those who might be scared away by an initially tough problem, is there a way I can interview you to translate a few of these high-level math concepts into plain language?

This is a project I’m working to develop a question framework to gain useful insight into a complex field in 20 questions or less to someone who is completely unfamiliar with the field.

The initial version of the question framework itself is here:

I understand you’re extraordinarily busy so I don’t expect you to reply but if you do have a few minutes to look it over, I think it’s a worthwhile endeavor and feedback from you is welcome.